Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-5x+6y &= 9 \\ 5x-2y &= -6\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $4y = 3$ Divide both sides by $4$ and reduce as necessary. $y = \dfrac{3}{4}$ Substitute $\dfrac{3}{4}$ for $y$ in the top equation. $-5x+6( \dfrac{3}{4}) = 9$ $-5x+\dfrac{9}{2} = 9$ $-5x = \dfrac{9}{2}$ $x = -\dfrac{9}{10}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{3}{4}$.